1918 
W2.4- 


WARNER 

ThE  PRESSURE  (NCR EASE 
IN  THE  CORONA. 


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UNIVERSITY   OF  ILLINOIS 
THE  GRADUATE  SCHOOL 


F  e  ftrnaryLJa  191  8 


I  HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY  SUPER- 
VISION BY   _  EA^L.&.~^ap.AC2...-"uJLg^^E  

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DEGREE  OF  DOCTOR  OF  PHTT.ORDPWY  TW  PHVfiTHR   


Head  of  Department 


Recommendation  concurred  in  :* 


Committee 
on 

Final  Examination* 


^Required  for  doctor's  degree  but  not  for  master's. 


THE  PRESSURE  INCREASE 
IN  THE  CORONA 


BY 


EARLE  HORACE  WARNER 

A.  M.  University  of  Illinois,  1914 
A.  B.  University  of  Denver,  1912 


THESIS 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE 
REQUIREMENTS  FOR  THE  DEGREE  OF 

DOCTOR  OF  PHILOSOPHY  IN  PHYSICS 


IN 


THE  GRADUATE  SCHOOL  OF  THE 
UNIVERSITY  OF  ILLINOIS 

1918 


PRESS  OF 
THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 


I 


(  Reprinted  from  the  Physical  Review,  N.S.,  Vol.  VIII.,  No.  3,  September,  1916:  and 
Vol.  X.,  No.  5,  November.  1917.) 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 

By  Earle  H.  Warner. 

L  Introduction. 

THE  "corona"  is  the  glow  which  surrounds  conductors  when  there 
exist  high  potential  differences  between  them  and  neighboring 
bodies.  A  careful  study  of  the  corona  phenomena  is  necessary  (1)  to 
determine  the  factors  which  regulate  the  loss  of  power  due  to  the  corona, 
which  on  long  transmission  lines  may  be  an  important  item,  and  (2)  to 
obtain  data  from  which  a  theory  can  be  developed  which  will,  with 
mathematical  rigor,  explain  the  corona  effects.  The  first  of  these  objects 
has  been  quite  successfully  carried  out  by  Peek,  Whitehead,  Ryan  and 
others.  The  only  advances  toward  a  theoretical  explanation  of  the  corona 
have  been  made  by  Bergen  Davis1  and  Townsend.2  In  these  two  theories 
the  authors  have  assumed  that  the  corona  is  an  ionization  phenomenon. 
That  is,  they  assume  that  the  high  potential  difference  causes  the  few 
ions  which  are  always  present  in  a  gas  to  move  with  a  velocity  sufficiently 
great  to  break  the  molecules  with  which  they  collide  into  two  parts,  one 
bearing  a  positive  charge  and  one  a  negative  charge.  All  these  charged 
particles  then  move,  because  of  the  influence  of  the  field,  toward  one  or 
the  other  of  the  terminals.  The  presence  of  these  ions  thus  explains  the 
conductivity  of  the  gas  and  the  acceleration  of  the  ions  explains  the 
light  effect.  If  the  corona  is  an  ionization  phenomenon  one  would 
expect,  if  the  corona  apparatus  was  inclosed,  at  the  instant  the  corona 
appeared,  i.  e.,  at  the  instant  the  molecules  were  broken  up  into  ions,  that 
the  pressure  in  the  apparatus  would  increase;  because  according  to 
kinetic  theory  the  greater  the  number  of  particles  in  a  given  volume  the 
greater  the  pressure.  This  pressure  increase  was  first  discovered  by 
Dr.  S.  P.  Farwell,3  working  in  this  laboratory  and  has  been  discussed 

3  "The  Corona  Produced  by  Continuous  Potentials,"  Proc.  A.  I.  E.  E.,  November.  1014 

later  by  J.  Kunz.4  The  above  mentioned  theories  assume  ionization 
but  do  not  account  for  such  a  pressure  increase.    Under  certain  circum- 

1  "Theory  of  the  Corona,"  Proc.  A.  I.  E.  E.,  January.  191 1. 

2  "The  Discharge  of  Electricity  from  Cylinders  and  Points,"  Phil.  Mag..  May,  1914. 

4  Dr.  Jakob  Kunz,  "On  the  Initial  Condition  of  the  Corona  Discharge,"  Phys.  Rev. 
July,  1916. 

3 


Ukii .  in 


4 


EARLE  H.  WARNER, 


stances  this  pressure  increase  can  amount  to  as  much  as  three  cm.  of 
mercury.  Arnold1  has  contended  that  the  pressure  increase  could  be 
completely  accounted  for  as  the  result  of  Joule's  heat,  and  that  the 
assumption  that  it  is  due  to  ionization  is  untenable.  To  support  this 
contention  Arnold  performed  experiments  "  by  electrically  heating  the 
central  wire  in  apparatus  similar  to  Harwell's  and  "  observed  the  pressure 
increase.  With  such  an  apparatus  Arnold  attempted  to  show  (i)  that 
an  increase  in  pressure  due  to  heat  appears  suddenly,  (2)  that  for  a  given 
power  consumed  in  the  tube  the  increase  in  pressure  due  to  heat  is  of 
about  "  the  same  magnitude  as  those  observed  "  in  the  corona. 

In  order  to  show  clearly  that  the  pressure  increase  is  not  due  to  heat 
a  series  of  comparative  experiments  were  performed  with  the  pressure 
increase  caused,  first,  by  producing  the  corona  glow  on  the  wire  and, 
second,  by  heating  the  central  wire.  The  pressure  increase  observed  in 
the  first  set  of  experiments  will  be  referred  to  as  caused  by  corona  and  in 
the  second  set  as  caused  by  heat. 

A  few  computations  have  also  been  made  which  strengthen  the  results 
of  the  experiments. 

Since  the  conception  of  ionization  is  so  intimately  associated  with  the 
idea  of  increase  in  pressure,  it  seemed  important  to  determine  the  laws, 
relating  this  ionization  pressure  to  the  corona  current. 

II.  Theory. 

Dr.  J.  Kunz  has  developed  a  theory  which  predicts  how  this  pressure 
increase  should  vary  with  the  current.  One  can  best  understand  his 
development  by  thinking  of  the  corona  as  occurring  around  a  wire  which 
is  coaxial  with  a  cylinder.    See  Fig.  1,  which  represents  a  cross  section 


U 




C 


-V 


Fig.  1.  •  Fig.  2. 

of  such  a  corona  tube.  Suppose  the  ends  of  the  tube  to  be  closed,  so 
as  to  inclose  a  constant  volume  uc.  When  the  wire  is  connected  to  a 
very  high  positive  potential  and  the  case  grounded  the  corona  glow- 
appears  around  the  wire  and  the  pressure  instantly  increases  from  at- 
1  H.  D.  Arnold,  (Abstract)  Phvs.  Rev.,  Jan.,  1917. 


I 

_J  V 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 


5 


mospheric  to  some  higher  value.  Let  the  condition  of  the  gas  at  the 
beginning  of  the  experiment  be  represented  by  the  point  A,  on  the  p  —  v 
plane.    (See  Fig.  2.)    The  volume  is  then  v0  and  the  pressure  p0. 

Step  I. — Apply  a  potential  difference  e  between  the  wire  and  the  case. 
Some  current  i  will  flow  and  the  pressure  will  immediately  jump  from  p0 
to  a  higher  value,  say  pi.  The  state  of  the  gas  will  now  be  represented 
by  the  point  C.  The  work  done  by  the  current  per  second,  ei,  will 
then  be  equal  to  the  increase  of  internal  energy  of  the  gas  A  U,  plus  the 
work  done  by  the  gas  Wu  due  to  the  pressure  increase.  This  energy 
equation  gives  us 

ei  =  AU  +  Wl  (i) 

Step  II. — Let  us  force  into  the  tube  a  small  amount  of  gas.  This 
will  require  work  dW2  and  the  pressure  will  increase  from  pi  to  pi  +  dpi 
and  can  be  represented  by  the  state  point  B.  Then 

dW-,  =  —  Vodpi.  (2) 

The  total  work  to  change  the  gas  from  state  A  to  state  B  has  then  been 

ei  +  dW-z  =  AU  +  \\\  -  v«dpi-  (3) 

Now  let  us  start  again  with  the  same  initial  conditions  and  by  two 
different  steps  arrive  at  the  same  final  condition. 

Step  III. — When  the  state  of  the  gas  is  A  let  us  force  in  a  small  amount 
of  gas.  This  will  require  work  dW3  and  the  pressure  will  increase  from 
po  to  p0  +  dpo,  which  may  be  represented  by  the  state  point  D.  Then 

dWz  =  -  vodp0.  (4) 

In  the  existing  conditions  the  size  of  the  current  depends  not  only  on 
the  potential  difference  but  also  upon  the  initial  and  final  pressures. 
The  increase  in  current  causes  an  increase  in  pressure  which  tends  to 
stop  the  current.  The  steady  condition  of  the  current  represents  a 
condition  of  equilibrium  between  the  attempt  of  the  current  to  increase 
the  pressure  and  the  attempt  of  the  increased  pressure  to  stop  the  current. 

Step  IV.  Now  apply  the  same  potential  difference  e.  Let  that 
current  i'  flow  so  that  it  will  cause  the  pressure  to  increase  from  po  +  dp* 
to  pi  +  dpi,  that  is,  so  that  the  state  of  the  gas  can  be  represented  by  B. 
Then  as  in  Step  I. 

ei'  =  AU'  +  Wt.  (5) 

In  the  last  two  steps  the  total  work  required  to  change  the  state  of 
the  gas  from  A  to  B  is 

ei'  +  dWs  =  AU'  +  W4  -  vdp0.  (6) 

Then  by  the  law  of  the  conservation  of  energy,  the  work  required  to 


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6 


EARLE  H.  WARNER. 


change  a  system  from  one  state  to  another  is  independent  of  the  path, 
we  have 


At/  +  Wx  -  vodp!  =  At/'  +  W,  -  vudpo 


or 


At/  -  At/'  +  Wx  -  Wi  =  v0(dp,  -  dp0). 
Subtracting  t5)  from  (i)  we  have 

At/  -  At/'  +  W\  -  WA  =  e(i  -  V). 


Therefore 

But 

Then 

and  integrating 


e(i  —  i')  -  Vo(dp!  —  dp0). 
i  =  V  +  di. 
edi  =  v0d(pi  —  po) 

Vq 

ki  =  —  (pi  —  po)  +  a  constant. 


(7) 
(8) 

(9) 
(10) 

(II) 

(12) 


Since  (pi  —  po)  represents  the  increase  in  pressure,  that  is,  the  ioniza- 
tion pressure,  this  equation  shows  that  the  ionization  pressure  should  be 
exactly  proportional  to  the  corona  current. 

It  was  the  object  of  the  experiments  which  have  been  performed  to 
test  this  relationship  with  pure  gases  in  the  tube. 

III.  Apparatus. 

The  constant  potentials  were  obtained  from  a  battery  of  continuous 
current  shunt-wound  500-volt  generators  connected  in  series. 

The  corona  tube  was  of  the  wire  and  coaxial  cylinder  type.    (See  Fig. 


Fig.  3. 


■una  aw  ^i)  moil  (?J  ^nhomtduS 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 


7 


3.)  Glass  plates  with  holes  for  the  wire  to  pass  through  were  sealed  to 
the  ends  of  the  tube  so  that  the  holes  were  on  the  axis  of  the  cylinder. 
The  wire,  No.  32,  copper,  passed  through  the  holes  and  was  thus  coin- 
cident with  the  axis  of  the  cylinder.  The  wire  was  sealed  into  these 
holes  and  held  taut  by  red  sealing  wax.  To  the  cylinder  was  soldered  a 
small  1!T"  tube,  one  side  of  which  was  joined  to  the  vacuum  pump  and 
the  other  side  Was  connected  to  a  Bristol  aneroid  pressure  gauge. 

The  increase  in  pressure  was  measured  by  this  Bristol  gauge.  Any 
increase  in  pressure  caused  it  to  bend  slightly  and  so  rotate  the  mirror. 
By  observing  the  deflection  of  a  beam  of  light  over  a  scale,  which  had 
previously  been  calibrated  by  reading  simultaneously  the  deflected  beam 
and  a  water  manometer  connected  directly  to  the  gauge,  the  increase  in 
pressure  in  cm.  of  water  could  be  determined.  The  advantage  of  such  a 
pressure  measuring  instrument  in  this  experiment  is  that  it  is  very  quick 


Maotun»  Tenoinaio. 


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V»Ur»,.«r. 


Y"ltch. 


Pole 

—  Cl  PGbongur 


Ga\v*nomo 
Braaa 


Fig.  4. 


in  its  action.  The  instant  the  pressure  increases  the  gauge  jumps  right- 
up  to  its  new  position  and  a  reading  can  be  taken  in  a  very  few  seconds. 
It  was  necessary  to  read  this  pressure  increase  quickly  because  if  much 
time  was  required,  the  heating  effect  of  the  current  would  increase  the 
pressure  also. 

The  current  was  measured  by  a  Type  H  D'Arsonval  galvanometer. 
The  apparatus  was  connected  as  is  shown  in  Fig.  4. 


EARLE  H.  WARNER. 


.  1 .50 


.1.25 


0  30  40  50 
Time  in  Seconds. 


Fig.  5. 


IV.    Experimental  Results. 

1 .  The  reason  why  one  who  sees  this  pressure  increase,  as  recorded  by 
a  quick-acting  pressure  meter,  thinks  it  is  not  a  heat  effect,  is  because  of 
rapidity  with  which  it  appears  and  disappears.  Arnold  showed  that  the 
pressure  increase  occurred  quite  rapidly  when  caused  by  heat.  The 
following  curves  show  the  difference  in  the  rapidity  of  appearance  and 
disappearance  of  the  pressure  increase  caused  by  heat,  and  caused  by 
corona.    It  will  be  noticed  in  Fig.  5,  where  the  pressure  increase  was 

caused  by  heating  the  central  wire,  that 
fifteen  seconds  was  required  for  the 
pressure  to  come  to  its  maximum  value, 
and  that  from  the  time  the  current  was 
broken  twenty-five  seconds  was  required 
for  the  pressure  to  return  to  practically 
its  original  value,  while  in  Fig.  6,  where 
the  pressure  increase  was  caused  by  co- 
rona, only  three  seconds  was  required 
for  the  maximum  pressure  to  be  at- 
tained and  that  the  pressure  came  back 
to  practically  its  original  value  in  eigh- 
teen seconds.  In  this  last  case  from  the 
appearance  of  the  phenomenon  it  seems,  if  the  aneroid  pressure  me- 
ter had  less  inertia,  that  the  pressure  increase  could  be  determined  in 
less  than  three  seconds.  These  curves  show  that  the 
pressure  increase  appears  five  times  as  rapidly  when 
caused  by  corona  as  when  caused  by  heat,  and  disap- 
pears also  more  rapidly. 

2.  In  the  pressure  increase  due  to  corona,  a  short 
time  interval  of  five  to  seven  seconds  occurs  after  the 
sudden  increase  of  pressure,  before  the  heat  effect  in 
the  corona  begins  to  be  noticed.  This  is  shown  by  an 
abrupt  bend,  A,  in  the  curve  where  the  pressure  in- 
crease is  plotted  against  time,  as  is  done  in  Fig.  7. 
No  such  bend  occurs  in  the  case  where  the  pressure 
increase  is  caused  by  heat  alone,  as  is  shown  in  Fig.  5.  In  the  work  which 
has  previously  been  reported  the  pressure  increase  measurements  were 
always  taken  at  the  point  A ,  and  this  seems  to  be  practically  independent 
of  the  heat  effect. 

3.  The  heat  which  is  produced  in  the  corona  discharge,  shown  by  the 
gradual  pressure  increase  from  B  to  C,  Fig.  7,  is  distributed  throughout  the 
whole  volume  of  enclosed  air  and  so,  when  the  current  is  broken  does  not 


Preesure  Incr«aeo 
Due  To  Corona . 


C  1-25 


0.75 


Time  in  See . 


Fig.  6; 


H  fetGOq 

n't  amh 
i!'jbf"»wa 


if 


THE  PRESSURE  INCREASE  IN  THE  CORONA, 


radiate  rapidly  because  the  air  is  a  poor  conductor.  This  is  shown  very 
clearly  in  Fig.  8.  This  seems  to  show  that  the  pressure  increase  due  to 
heat  in  the  corona  is  represented  by  the  difference  of  ordinates  of  C  and 
B  (Fig.  8).  As  soon  as  the  corona  current  is  broken  at  C  the?  increase 
in  pressure  due  to  corona  at  once  disappears,  but  the  increase  in  pressure 


Pressure  Increase  Due  To  Corona. 


10      20      JO      4o      50      60       70      to  90 
Time  In  Seconds. 


20      40      60      CO     100     120     140     160     1*0  200 
Time  in  Seconds. 


Fig.  7. 


Fig.  8. 


due  to  heat  in  the  corona  discharge  remains,  as  is  shown  by  the  difference 
of  ordinates  of  D  and  A.  This  difference  is  always  very  nearly  equal  to 
the  difference  of  ordinates  of  C  and  B.  This  heat  energy  produced  by 
the  corona  current,  since  it  is  distributed  through  the  gas,  radiates  very 
slowly,  as  is  shown  by  the  gradual  descent  of  the  curve  from  D  to  E. 
No  such  effect  is  observed  when  the  increase  of  pressure  is  due  entirely 
to  heat,  as  is  shown  in  Fig.  5.  This  curve  (Fig.  5)  shows  that  twenty-five 
seconds  after  the  current  through  the  wire  is  broken  at  C  the  resultant 
pressure  increase  due  to  heat  has  practically  disappeared;  while  Fig.  8 
shows  that  twenty-five  seconds  after  the  corona  is  removed  from  the  wire 
the  increase  in  pressure  due  to  the  corona  has  disappeared,  but  practically 
all  the  pressure  increase  due  to  heat  in  the  corona  (ordinates  C  minus  B 
approximately  equals  ordinates  D  minus  A)  still  remains  and  radiates 
very  slowly. 

4.  If  the  increase  in  pressure  is  due  to  heat,  the  same  increase  in 
pressure  should  result  when  the  same  power  is  consumed  (<z)  with  a 
corona  current  through  the  gas,  (b)  with  a  heating  current  through  the 
wire.  Figs.  9  and  10  show  that  this  is  not  the  case.  The  powers  con- 
sumed in  the  two  cases  are  not  exactly  the  same,  but  one  can  see  that  were 
they  the  same,  the  increase  in  pressure  due  to  corona  would  be  approxi- 
mately one  half  the  increase  in  pressure  due  to  heat.  The  power  in  the 
c  ise  of  the  corona  was  obtained  by  multiplying  the  potential  difference 
between  the  wire  and  the  tube  by  the  corona  current,  and  in  the  case  o£ 


IO 


EARLE  H.  WARNER; 


the  heated  wire  was  obtained  by  multiplying  the  current  through  the 
wire  by  the  potential  difference  across  that  portion  of  the  wire  which  was 
in  the  tube. 

5.  If  the  increase  in  pressure  in  the  corona  discharge  is  due  to  heat  the 
temperature  of  the  air  in  the  corona  tube  must  increase.  This  may  or 
may  not  be  the  case  in  the  luminous  layer  near  the  wire  but  the  tern- 


Pressure  Increaoo  Due  To  Corona 
0.266  Watts. 


10      20      50      40      50  60 
Tine  In  Seconds. 


10      20      JO      40      50      60      70      $0      90  100 
Time  la -Seconds. 


Fig.  9. 


Fig.  10. 


01  ffi 
U  W 

3  c 

♦"•nCooXing  Effect  in  Corona 
as  *o 
t<  m 
©  o 


5§ 

o 

01  c 

<0  0) 


Tims  in  See 
10  20 


/f 


perature  of  the  gas  in  the  tube  at  a  point  four  millimeters  from  the  wire 
actually  decreases.  This  was  determined  by  inserting  a  sensitive  ther- 
mocouple made  of  very  fine  Copper-Advance  wire  into  the  corona  tube. 
The  temperature  decreased  only  at  the  instant  the  corona  appeared.  In 
a  short  time,  after  the  heat  due  to  the  corona  began  to  appear  (corre- 
sponding to  the  slope  B  to  C,  Figs.  7  and  8)  the  temperature  of  the  gas 
in  the  tube  began  to  increase.  This  cooling  effect  is  shown  in  Fig.  1 1. 
Comparing  Figs.  1 1  and  7  it  is  seen  that  the  increase  in  pressure  which 

was  measured  at  A  was  observed  while  there 
was  an  actual  cooling  in  the  corona  tube. 
This  cooling  should  be  expected  when  air  or 
oxygen  are  in  the  tube,  for  under  these  condi- 
tions ozone  is  formed.  Since  the  formation  of 
ozone  from  oxygen  is  always  accompanied  with 
an  absorption  of  heat  the  temperature  of  the 
air  or  oxygen  would  tend  to  lower.  Mr.  J. 
W.  Davis,  working  on  corona  about  hot  wires 
in  hydrogen,  has  discovered  that  the  appearance  of  the  corona  about  a 
tungsten  wire  heated  to  white  heat,  causes  it  to  cool  to  dull  red.  This 
tends  to  show  that  even  in  the  corona  glow  itself  there  is  a  cooling  effect. 

6.  If  the  increase  in  pressure  in  the  corona  is  due  to  heat  one  should 
expect  it  to  be  the  same  with  the  wire  either  positive  or  negative.  It 
will  be  mentioned  below,  that  it  is  impossible  to  obtain  measurements 
when  the  wire  is  negative  because  of  the  presence  of  beads.  The  negative 
corona  is  entirely  different  from  the  positive  corona. 

7.  The  following  consideration  will  further  show  that  the  increase  in 


Fig.  11. 


OJ 


.Q  .8n 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 


pressure  can  not  be  due  to  heat.  The  heat  produced  by  the  corona 
current  will  be  given  by  the  equation  H  —  0.238  eit  and,  if  the  observed 
pressure  increase  is  due  to  heat,  the  increase  in  pressure  Ap  will  be  pro- 


5  6  7 

Current  la  10"*  Aaperea. 

Fig.  12. 

portional  to  the  heat,  and  we  can  write  Ap  =  k  eit.  Now  the  only  way 
for  Ap  to  vary  directly  as  i,  the  corona  current,  as  is  the  case — shown  by 
curves  in  the  next  paragraph — is  for  e  to  be  independent  of  i.  Data 
shows  that  this  is  not  the  case. 


Relation  B«tw«en 
I0H12ATI0U  PRESSURE  and  CORONA  CURRXHT, 
Nitrogen*    Ylra  +. 

Currant  In  10-*  *mpor««. 

Fig.  13. 


r 


: 


- 

.11  .sit 


EARLE  It.  WARNER. 


8..  To  determine  the  laws  relating  this  ionization  pressure  to  the  corona 
current  experiments  were  made  when  the  wire  was  positive  and  the  case 
grounded  with  dry  air,  hydrogen,  nitrogen,  carbon  dioxide,  oxygen  and 
ammonia  as  the  gases  in  the  tube.  Considerable  care  was  taken  to  see 
that  these  gases  were  absolutely  pure.  They  were  all  dried  carefully 
before  they  were  used.    The  following  curves  (Figs.  12,  13,  14,  15,  16) 


7    a   9    10  11  12. 

Ourreat  In  I 0"8  Aap«re» 


Fig.  14. 

show  graphically  the  results.  Fig.  17  shows  all  the  curves  plotted  to 
the  same  scale.  With  this  scale  the  hydrogen  curve  should  be  continued 
until  its  ordinate  is  equal  to  that  of  the  carbon  dioxide  curve. 

The  fact  that  the  points  all  lie  so  accurately  on  a  straight  line  shows 
conclusively  that  experiment  verifies  the  prediction  made  by  Dr.  Kunz's 
theory.  The  law  can  then  be  stated  that,  in  the  gases  studied  with  the 
wire  positive  the  ionization  pressure  is  exactly  proportional  to  the  corona 
current. 

In  the  case  of  oxygen  a  considerable  amount  of  ozone  was  formed  due 
to  the  corona  discharge.  Evidently  the  curve  as  shown  is  a  resultant 
of  two  effects:  (1)  A  chemical  change  due  to  the  formation  of  ozone. 
This  would  tend  to  cause  a  decrease  in  pressure.  (2)  The  increase  in 
pressure  due  to  the  ionization  of  the  oxygen.  Since  the  ionization  curve 
is  a  straight  line,  as  is  shown  by  the  gases  in  which  probably  there  is  no 
chemical  action,  and  since  this  resultant  curve  of  oxygen  is  a  straight 
line,  the  following  law  can  be  stated  : 

Whenever  chemical  change  takes  place  due  to  the  corona  the  chemical 
change  is  exactly  proportional  to  the  current. 


S  I 


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THE  PRESSURE  INCREASE  IN  THE  CORONA. 


13 


With  the  wire  negative  beads  always  appear  on  the  wire,  and  since  the 
pressure  increase  varies  with  the  arrangement  of  the  beads  which  are 
not  stable,  it  is  impossible  to  accurately  verify  the  above  relationship. 
When,  instead  of  the  quick  acting  gauge,  an  ordinary  open  manometer 


Relation  Between 
IONIZATIOB  PRESSURE  and  C0B03A  CtJRKEHT. 
Oxygen.  Tire  +. 


Current  in  10"5  Amperee. 

Fig.  15. 


which  is  slow  in  its  action  was  used,  it  was  discovered  that  the  same 
relationship  as  above  stated  is  very  nearly  true  for  the  wire  negative  as 
well  as  positive. 

The  increase  in  pressure  in  the  case  of  nitrogen,  showing  ionization, 


Relation  Between 
IONIZATION  PRESSURE  and  COR OS A  CURRENT. 
Ammonia,      Wlr*>  *« 

Fig.  16. 


is  one  of  the  exceptional  cases  where  nitrogen  is  largely  ionized  at  lo\ 
temperatures  and  thus  probably  chemically  active. 


X 

S  i 


14 


EARLE  H.  WARNER. 


How  nitrogen,  carbon  dioxide  and  ammonia  are  ionized,  are  questions 
which  require  further  study. 

The  arrangement  of  the  apparatus  could  be  used  as  a  high  potential 
voltmeter  by  simply  calibrating  the  increase  in  pressure  against  volts,  as 
determined  by  a  disc  electrometer. 


6 

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£  2. 

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Relation  Between 
I0HI2ATI0B  PRESSURE  and  CORONA  CURRENT 
Tire  +. 


T3  2. 

Currant  la  10'*  Aaperot. 


Fig.  17. 


V.    Results  from  Theoretical  Considerations. 

1.  If  the  increase  in  pressure  is  due  to  heat  it  is  possible  to  compute 
the  magnitude  of  the  pressure  increase  when  one  knows  the  watts  of 
electrical  energy  consumed  in  the  tube.  The  trial  represented  in  Fig.  io 
gives  us  this  data.  The  observed  pressure  increase  was  measured  in 
three  seconds  so  that  the  total  number  of  joules  of  work  consumed  by 
the  tube  in  that  time  was  3  X  0.266  =  0.798  joules  and  this  corresponds 
to  6.1909  calories.  Knowing  the  volume  of  the  tube,  the  temperature 
and  pressure  of  the  air  in  it,  the  mass  of  the  air  in  the  tube  can  be  com- 
puted. With  the  above-mentioned  quantity  of  heat  and  mass  of  air, 
together  with  the  specific  heat  of  the  air  at  constant  volume,  the  temper- 
ature rise  of  the  air  can  be  computed,  assuming  that  the  electrical  energy 
is  converted  into  heat.  This  temperature  rise  comes  out  to  be  2. 44°  C, 
which  at  constant  volume  corresponds  to  a  pressure  increase  of  about 
nine  cm.  of  water,  while  the  observed  pressure  increase  in  this  particular 
trial  amounts  to  about  seven  tenths  cm.  of  water.  In  this  computation 
radiation  and  conduction  losses  have  been  neglected  because  they  would 
be  very  small  from  a  body  2.440  C.  above  room  temperature.  This 
shows  that  the  observed  results  lie  in  a  different  order  of  magnitude  from 
what  would  be  expected  if  Arnold's  theory  were  true. 

2.  Arnold  states,  if  "  we  compute  the  corona  currents  that  would 
result  from  the  presence  of  enough  ionized  particles  to  produce  the  ob- 


.flRWIKYI  .Yl  CUflKTV 


- 

THE  PRESSURE  INCREASE  IN  THE  CORONA. 


1600 


served  pressure  changes,  the  currents  calculated  are  many  thousand  times 
greater  than  those  actually  obtained."  Such  a  statement  is  only  true 
when  the  ionized  particles  are  produced  in  a  uniform  or  practically  uni- 
form electric  field.  This  is  not  the  case  in  the  corona  tube.  H.  T.  Booth 
is  publishing  data  on  the  distortion  of  the  field  in  the  corona  tube.  This 
data  shows  that  the  potential  gradient  near  the  wire  is  very  high — of  the 
order  of  30,000  volts  per  cm.  This  is  the  arcing  gradient,  in  which  it  is 
probable  every  molecule  is  ionized.  Then  for  a  long  space  between  the 
wire  and  the  tube  there  is  a  very  small  gradient.  With  this  condition 
of  the  field,  near  the  wire  every  molecule  may  be  ionized  and  still  the 
resultant  current  be  very  small,  for  few  of  the  ionized  particles  near  the 
wire  will  pass  through  the  space  where  there  is  a  small  gradient.  Simple 
computations  based  on  kinetic 
theory  show  that  the  maximum 
observed  pressure  increases  can 
be  explained  by  ionization  if 
every  molecule  of  the  air  with- 
in 1.39  mm.  of  the  wire  is 
ionized.  Within  this  distance 
the  potential  gradient  is  equal 
to  the  arcing  gradient  and 
therefore  probable  that  all  mole- 
cules are  ionized. 

VI.    Further  Verification 

of  Kunz's  Theory. 
The  final  equation  as  pre- 
sented above  is 

Do 

ki  =  —  (pi  —  po)  +  a  constant, 

where  i  is  the  corona  current, 
v0  the  volume  of  the  tube,  e 
the  potential  difference  between 
the  wire  and  the  tube,  px  —  p0 
the  pressure  increase,  k  a  con- 
stant and  p0  the  initial  pressure.  This  equation  shows  that  for  a  con- 
stant potential  difference  e,  the  current  i  should  increase  as  p0  is  low- 
ered. Data  was  taken,  by  measuring  the  current  at  various  measured 
pressures,  caused  by  a  constant  potential  difference,  which  verifies  this 
theory.  This  data  is  shown  graphically  in  Figs.  18  and  19  when  pure 
hydrogen  and  nitrogen  respectively  were  the  gases  in  the  tube. 


400 


540  440  J40~ 

Pressure  In         of  Maroury. 


Fig.  18. 


16 


EARLE  H.  WARNER. 


VII.  Summary  and  Conclusions. 
Experimental  results  show: 

1.  That  the  increase  in  pressure  due  to  corona  appears  and  disappears 
much  more  rapidly  than  when  due  simply  to  heat. 

2.  That  the  heat  in  the  corona  discharge  is  not  a  prominent  factor 
until  many  seconds  after  the  corona  appears. 

3.  That  in  equal  energy  experiments  the  increase  in  pressure  due  to 
corona  differs  from  the  increase  in  pressure  due  to  heat[by  about  50  per 
cent. 

4.  That  at  the  instant  the  corona  appears  the  gas  injthe  tube  at  a 
small  distance  from  the  wire  is  cooled. 


TB" 720 680 640  600  560  520 

PresuuTO  In  Hro.  of  lioroury. 

Fig.  19. 

5.  The  ionization  pressure  in  the  positive  corona  is  exactly  proportional 
to  the  corona  current  in  dry  air,  hydrogen,  nitrogen,  carbon  dioxide, 
oxygen  and  ammonia. 

6.  Any  chemical  action  that  takes  place  due  to  the  corona  is  exactly 
proportional  to  the  corona  current. 

7.  That  the  theory  advanced  by  Kunz  is  verified  in  one  more  field, 
namely  in  the  relation  between  current  and  pressure  for  constant  voltage. 

These  results  together  with  conclusions  drawn  from  simple  calculations, 
force  one  to  believe  that  the  pressure  increase  in  the  corona  discharge  is 


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THE  PRESSURE  INCREASE  IN  THE  CORONA. 


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not  due  to  Joule's  heat.  With  the  recent  knowledge  of  the  distortion  of 
the  field  in  the  corona  tube  it  seems  very  possible  that  the  increase  in 
pressure  is  due  to  ionization. 

The  writer  desires  to  express  his  appreciation  to  Professor  A.  P.  Carman 
for  the  use  of  the  laboratory  facilities,  and  to  Dr.  Jakob  Kunz  for  his 
continued  interest  and  suggestions. 
Laboratory  of  Physics, 
University  of  Illinois, 
June.  1917. 


.fiQi  .sauL 


VITA. 

Earle  Horace  Warner  completed  his  secondary  training  at  the  Manual 
Training  High  School  of  Denver,  Colorado.  In  1908  he  entered  the 
L  diversity  of  Denver  and  from  it,  in  1912,  received  his  A.B.  degree. 

Since  1912  he  has  been  a  graduate  student  at  the  University  of  Illinois. 
In  1914  he  received  the  degree  of  A.M.  from  the  University  of  Illinois. 

He  has  held  the  following  positions:  Assistant  in  Physics,  University 
of  Denver,  1910-1912;  Assistant  in  Physics,  University  of  Illinois, 
1912-1917;  Instructor  in  Physics,  University  of  Illinois,  191 7  1918. 

He  has  published  the  following  papers:  "Determination  of  the  Laws 
Relating  Ionization  Pressure  to  the  Current  in  the  Corona  of  Constant 
Potentials,"  Physical  Review,  N.S.,  Vol.  VIII.,  No.  3,  p.  285,  1916: 
"The  Pressure  Increase  in  the  Corona,"  Physical  Review,  N.S.,  Vol. 
10,  No.  5,  p.  483,  1917. 


